(2y+1)(5-y)=0

Solution for (2y+1)(5-y)=0 equation:

Simplifying
(2y + 1)(5 + -1y) = 0

Reorder the terms:
(1 + 2y)(5 + -1y) = 0

Multiply (1 + 2y) * (5 + -1y)
(1(5 + -1y) + 2y * (5 + -1y)) = 0
((5 * 1 + -1y * 1) + 2y * (5 + -1y)) = 0
((5 + -1y) + 2y * (5 + -1y)) = 0
(5 + -1y + (5 * 2y + -1y * 2y)) = 0
(5 + -1y + (10y + -2y2)) = 0

Combine like terms: -1y + 10y = 9y
(5 + 9y + -2y2) = 0

Solving
5 + 9y + -2y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(5 + -1y)(1 + 2y) = 0

Subproblem 1
Set the factor '(5 + -1y)' equal to zero and attempt to solve:

Simplifying
5 + -1y = 0

Solving
5 + -1y = 0

Move all terms containing y to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + -1y = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1y = 0 + -5
-1y = 0 + -5

Combine like terms: 0 + -5 = -5
-1y = -5

Divide each side by '-1'.
y = 5

Simplifying
y = 5
Subproblem 2
Set the factor '(1 + 2y)' equal to zero and attempt to solve:

Simplifying
1 + 2y = 0

Solving
1 + 2y = 0

Move all terms containing y to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + 2y = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2y = 0 + -1
2y = 0 + -1

Combine like terms: 0 + -1 = -1
2y = -1

Divide each side by '2'.
y = -0.5

Simplifying
y = -0.5
Solution
y = {5, -0.5}